A fun brainteaser I came across at DiploBlogic. It reminded me of the now defunct analytic section from the GRE (which was, of course, my favorite part) . If you're stumped, you can find the answer over there!

THREE GODS

In a country long ago and far away there was a temple to which the people came to request the favor of the gods. In the temple there were three identical statues, and each statue could speak to worshippers on behalf of the god it represented. Though the three statues were identical in appearance, each represented a different god. One statue spoke for the God of Truth, and it always said the truth. Another spoke for the God of Falsehood, and what it said was always false. The third spoke for the God of Diplomacy; it sometimes spoke the truth, and sometimes did not.

The statues would answer any questions the people asked them, but of course different statues would give different answers to the same questions! Since no one knew which statue represented which god, interpreting the answers which the statues gave was pretty tricky, and there were a good many "religious experts" who claimed to be able to interpret the statues' answers and who charged high fees for their services. It seemed to most people, however, that these experts usually disagreed with each other.

One day a logic student appeared at the temple and announced that she knew how to discover which statue represented which god; it could be done by simply asking each statue one question. The answers would, she said, reveal which one answered truly, which one answered falsely, and which one was diplomatic.

So she entered the temple and stood before the three statues and asked the one on the left, "What god's statue is standing next to you?" The answer was: "The God of Truth." Then to the statue in the middle she said: "Which god do you represent?" The answer was, "The God of Diplomacy." And finally she said to the statue on the right, "What god's statue is standing next to you?" And the reply was, "The God of Falsehood."

"Aha!" said the logic student, "That makes it perfectly clear!" She then went into business as a religious expert and soon made a fortune interpreting the answers which the statues gave to people's questions, because it soon became obvious that her interpretations were always correct.